Transformity: The Dependence of the Laws of Physics on Higher-Dimensional Coordinate Transformations

Abstract

In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in (say) five dimensions is broader than in spacetime. This kind of gauge dependence is illustrated by two examples: a cosmological model in general relativity and a matter wave in quantum theory. Surprisingly, both are equivalent by coordinate transformations to flat featureless five-dimensional space. This kind of transformity is of fundamental significance for the philosophy of physics.